Legendre expansion method for the solution of the second-and fourth-order elliptic equations. (English) Zbl 1004.65120

Elbarbary, Elsayed M. E.

Math. Comput. Simul. 59, No. 5, 389-399 (2002).

A formula expressing Legendre polynomials in terms of their derivatives and a formula expressing a Legendre polynomial integrated \(k\)-times in terms of Legendre polynomials is presented. By using these formulae second- and fourth-order elliptic equations are solved. The numerical results are in good agreement with the exact solution.

Reviewer: Wilhelm Heinrichs (Essen)

MSC:

65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J40	Boundary value problems for higher-order elliptic equations
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
31A30	Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions

Keywords:

spectral methods; Legendre polynomials; Helmholtz equation; biharmonic equation; numerical results

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